Forced vibrations, resonance and dampingAQA A-Level Physics: Subtopic test

1. 1
   A child sits on a playground swing. When pushed once and left alone, the swing oscillates freely with a natural frequency of 0.50 Hz. A parent then pushes the swing at regular intervals, applying a small force each time.

   (a)

   The parent wants to make the amplitude of the swing as large as possible. What time interval should there be between successive pushes in the same direction?

   [1 mark]

   • A2.0 s
   • B0.50 s
   • C4.0 s
   • D3.1 s

   (b)

   The parent now pushes steadily at a frequency of 0.20 Hz. After the swing has settled into a steady motion, at what frequency does it oscillate?

   [1 mark]

   • A0.50 Hz
   • B0.35 Hz
   • C0.70 Hz
   • D0.20 Hz

   (c)

   Explain why the amplitude of the swing becomes very large when the parent pushes at 0.50 Hz.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A pedestrian footbridge has a natural frequency of 2.0 Hz for its vertical oscillations. When a large crowd crossed it on opening day, the bridge began to sway noticeably. Engineers have since fitted dampers containing viscous oil to the underside of the deck.

   (a)

   What is the effect of increasing the damping on the oscillations of the bridge when driven at its natural frequency?

   [1 mark]

   • AThe amplitude at resonance increases and the peak becomes sharper
   • BThe amplitude at resonance decreases and the peak becomes less sharp
   • CThe amplitude at resonance is unchanged but the natural frequency increases
   • DThe amplitude at resonance decreases and the peak becomes sharper

   (b)

   A group of soldiers marching in step could set up the largest oscillations in the bridge. Which marching rate is most dangerous?

   [1 mark]

   • A60 steps per minute
   • B90 steps per minute
   • C120 steps per minute
   • D240 steps per minute

   (c)

   Explain how the oil dampers make the bridge safer when large crowds cross it.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A tuning fork of frequency 512 Hz is held over the open end of a long glass tube that is closed at the bottom by water. The water level can be lowered to change the length of the air column. The speed of sound in air is 340 m s⁻¹ and end effects may be ignored.

   (a)

   The air column resonates strongly when the length of the column is a certain value. Explain how a stationary wave is formed in the tube and why resonance occurs.

   [3 marks]

   (b)

   Calculate the wavelength of the sound and the two shortest lengths of air column at which resonance occurs.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A technician tests a model of a car suspension. A mass supported by a spring is driven vertically by a vibration generator of constant driving force whose frequency can be varied. The natural frequency of the mass on the spring is 4.0 Hz.

   (a)

   The driving frequency is increased slowly from 1.0 Hz to 10 Hz with the driving force kept constant. Describe and explain how the amplitude of the mass varies.

   [6 marks]

   (b)

   An oil-filled shock absorber is now added to the suspension model and the test is repeated. Describe how the amplitude-frequency graph changes, and evaluate whether critical damping would be the best choice for the suspension of a real car.

   [6 marks]

   Total for question 4: 12 marks

End of questions